This paper tackles a critical challenge in data management: adapting to evolving user requirements, a concept we term evolution management. Our approach specifically addresses the evolution management of multi-model data. By leveraging category theory, we provide an abstract representation of the combined models. We extend this categorical framework by introducing schema-modification operations of varying types and complexities. And, we propose corresponding propagation strategies to adapt queries, with a particular focus on mitigating the impact of decreasing information capacity. Through experimental verification, we demonstrate significant reductions in effort across different strategies and their effects on querying.